You can get rid of Banana Trees by Digging out the stumps, rhizomes and roots is the best way to get rid of banana plants. Cut the trunks down to the ground and dig out the rest. This is a lot of work, but necessary. You may miss some small pieces. Watch the area and promptly remove any stray shoots you see come up.
In the future, watch for new shoots growing up on your side of the fence, and promptly dig them out. People should never plant bananas near their property line. The plants can easily spread into neighboring properties and become a nuisance.